单相正弦交流电路

单相正弦交流电路 4 单相正弦交流电路 【课题】 4.1 正弦交流电路的基本物理量 【教学目标】 描述正弦交流电的基本概念。了解正弦量的三要素。 【教学重点】 正弦交流电的三要素。 【教学难点】 正弦交流电的角频率、有效值、相位、初相位和相位差。 【教学过程】 【一、复习】 正弦函数及达形式。 【二、引入新课】 本节是正弦交流电的基础知识，是单相正弦和三相正弦交流电路的基础。要特别注意正弦交流电的“三要素”的理解和掌握。 【三、讲授新课】 4.1.1 交流电的基本概念 (1)交流电:大小和方向随时间作周期性变化，并且在一个周期内的平均值为零的电压、电流和电动势。图4.1画出了直流电和几种交流电的波形。 图4.1 直流电和交流电的波形 (2)直流电和交流电的表示:直流电的物理量用大写字母表示，例如:E、I、U等;交流电的物理量用小写字母表示，例如e、i、u。 (3)交流电的参考方向:如图4.2所示为交流电的参考方向。图中标出的u、i、u的方向均为s参考方向，它们的实际方向是在不断反复变化的，与参考方向相同的半个周期为正值，与参考方向相反的半个周期为负值。 图4.2 交流电的参考方向 the Communist Party of China, and a deep understanding of the party's nature, purpose, guiding principles, goals, organization, good style, deeply understand the conditions, rights and obligations of members, code of conduct, bearing in mind that oath, clear Members of the standards and conditions, enhance respect, abide by the Constitution, maintaining the party Constitution consciousness of the party Constitution. Read through the familiar with the code of self-discipline of the CPC, the CPC disciplinary regulations, members of the Communist Party of China party regulations on rights protection Ordinance, mastering self-discipline standards of "four must", the "four upholdings", mastering various types of disciplinary offence and punishment provisions and clear what you can do, what they can't do. 2. speech understanding learning series XI series the basic spirit of an important speech by General Secretary, learn to understand the Party Central Committee on governance of the new concept of basic elements of new ideas and new strategies, master and strengthen the party spirit, fulfills the purpose ideas, moral character, conservation related to the basic requirements. Learning of the XI series read the important speech by General Secretary (2016), XI Henan work research guide, General Secretary's important speech. Learning series speech, main understand master following aspects content: (1) ideal faith 4.1.2 正弦交流电相关量 1(周期:交流电变化一个循环所需要的时间，如图4.3所示。 2(频率:交流电在单位时间内(每秒钟)完成的周期数，单位是赫[兹](Hz)。频率和周期是互为倒数，即 1 , fT 图4.3 正弦交流电的波形 3(角频率:单位时间内变化的角度(以弧度为单位)，单位是弧度/秒(rad , s)。角频率与周期T、频率f之间的关系为 , , 2,f [例4.1] 我国供电电源的频率为50Hz，称为工业频率，简称工频，其周期为多少,角频率为多少, [解] 11T , s , 0.02s ,f50 , , 2 , f ,2 ， 3.14 ， 50 rad , s = 314 rad , s 即工频50 Hz的交流电，每0.02 s钟变化一个循环，每秒钟变化50个循环。 4(瞬时值:交流电每一瞬时所对应的值。 5(最大值:交流电在一个周期内数值最大的值。 6(有效值:规定用来计量交流电大小的物理量。如果交流电通过一个电阻时，在一个周期内产生的热量与某直流电通过同一电阻在同样长的时间内产生的热量相等，就将这一直流电的数值定义为交流电的有效值。 正弦交流电的有效值和最大值之间的关系为 ImI, , 0.707 I m2 一般情况下，人们所说的交流电流和交流电压的大小以及测量仪表所指示的电流和电压值都是指有效值。 [例4.2] 我国生活用电是220 V交流电，其最大值为多少, [解] 22U ,U , ， 220 V , 311 V m ,7(相位:正弦交流电流在每一时刻都是变化的，(ωt+)是该正弦交流电流在t时刻所对应的0 角度。 ,8(初相角:t , 0所对应的角度。 0 9(相位差:两个同频正弦交流电的相位之差。 , , ( , t + , ) , ( , t + , ) , , , , 01 02 01 02 若 0 , , , , 时，波形如图4.4(a)所示，i总比i先经过对应的最大值和零值，这时就称i超前121i , 角(或称i滞后i, 角)。 221 若, , , , , 0时，波形如图4.4(b)所示，称为i滞后于i(或称i超前i)。 1221 若 , , 0时，波形如图4.4(c)所示，称为i与i相位相同，简称同相。 12 speechpurpose ideas, moral character, conservation related to the basic requirements. Learning of the XI series read the important e of the new concept of basic elements of new ideas and new strategies, master and strengthen the party spirit, fulfills the ernancI series the basic spirit of an important speech by General Secretary, learn to understand the Party Central Committee on govry offence and punishment provisions and clear what you can do, what they can't do. 2. speech understanding learning series Xdiscipline standards of "four must", the "four upholdings", mastering various types of disciplina-tection Ordinance, mastering selfcipline of the CPC, the CPC disciplinary regulations, members of the Communist Party of China party regulations on rights prodis-lf, maintaining the party Constitution consciousness of the party Constitution. Read through the familiar with the code of seconduct, bearing in mind that oath, clear Members of the standards and conditions, enhance respect, abide by the Constitutionn, good style, deeply understand the conditions, rights and obligations of members, code of the Communist Party of China, and a deep understanding of the party's nature, purpose, guiding principles, goals, organizatiounderstand master following aspects content: (1) ideal faith by General Secretary (2016), XI Henan work research guide, General Secretary's important speech. Learning series speech, main2 , , , 时，波形如图4.4(d)所示，称为i与i相位相反，简称反相。 若 12 (a)0 , , , , (b), , , , , 0 (c) , , 0 (d) , , , 图4.4 正弦交流电的相位差 4.1.3 正弦交流电的表示法 1(波形图表示法 波形图表示正弦交流电:如图4.5所示。 图4.5 正弦交流电的波形表示法 ,图中直观的表达出被表示的正弦交流电压的最大值U，初相和角频率ω(ω = 2, f)。 m2(解析式表示法 用解析式表示正弦交流电为 ,u , Usin(, t +)= Usin ,m 0m ,,式中 , , , t ， ，,为该正弦交流电压的相位(ω为角频率，为初相角);U为最大值。 00m 3(旋转矢量表示法 旋转矢量表示正弦交流电:如图4.6所示。 图4.6 正弦交流电的矢量表示 ,图中矢量的长度表示正弦交流电的最大值(也可表示有效值);矢量与横轴的夹角表示初相，> 0 speech. Learning series speech, main understand master following aspects content: (1) ideal faithXI series read the important speech by General Secretary (2016), XI Henan work research guide, General Secretary's important e party spirit, fulfills the purpose ideas, moral character, conservation related to the basic requirements. Learning of the hen tharty Central Committee on governance of the new concept of basic elements of new ideas and new strategies, master and strengtderstanding learning series XI series the basic spirit of an important speech by General Secretary, learn to understand the Povisions and clear what you can do, what they can't do. 2. speech undiscipline standards of "four must", the "four upholdings", mastering various types of disciplinary offence and punishment pr-rty regulations on rights protection Ordinance, mastering selfdiscipline of the CPC, the CPC disciplinary regulations, members of the Communist Party of China pa-familiar with the code of self ct, abide by the Constitution, maintaining the party Constitution consciousness of the party Constitution. Read through theresped obligations of members, code of conduct, bearing in mind that oath, clear Members of the standards and conditions, enhance the party's nature, purpose, guiding principles, goals, organization, good style, deeply understand the conditions, rights an the Communist Party of China, and a deep understanding of3 , 0在横轴的下方;矢量以 , 角速度逆时针旋转。 0在横轴的上方，,0 π[例4.3] 将正弦交流电流i = 10 sin ( 314 t +) A用旋转矢量表示。 23 π[解] 选定矢量长度为10 ，与横轴夹角为，以314 rad , s的角速度逆时针旋转，可得旋转23 矢量如图4.7所示。 ππ[例4.4] 某两个正弦交流电流，其最大值为2A和3A，初相为和，角频率为ω，22,36作出它们的旋转矢量，写出其对应的解析式。 图4.7 例题4.3附图 图4.8 例题4.4附图 ππ[解] 分别选定2和3为矢量长度，在横轴上方和角度作矢量，它们都以同样ω角速2236 度逆时针旋转，如图4.8所示。它们所对应的解析式为 πi, 22sin (ωt + ) (A) 1 3 πi, 32sin (ωt , ) (A) 2 6 注意:不同频率的正弦交流电是不能画在一个图上的。所以矢量长度即可以使用最大值度量，也可以使用有效值度量。 【四、小结】 1(正弦量的三要素:频率、幅值和初相位。 2(初相位是确定正弦量初始值的，而且初相位因计时起点( t = 0 )取得不同而不同; 3(相位差是两个同频正弦交流电的初相位之差，它不随计时起点而变化; 4(初相位、相位差和相位都是电角度，但意义是不同的。 5(正弦交流电可以用波形表示法、解析式表示法和矢量表示法来描述。 【五、】 一、是非题:1、2、3;二、选择题:1、2、3、4;四、作图题:1、2。 understand master following aspects content: (1) ideal faith by General Secretary (2016), XI Henan work research guide, General Secretary's important speech. Learning series speech, main speechpurpose ideas, moral character, conservation related to the basic requirements. Learning of the XI series read the important e of the new concept of basic elements of new ideas and new strategies, master and strengthen the party spirit, fulfills the ernancI series the basic spirit of an important speech by General Secretary, learn to understand the Party Central Committee on govry offence and punishment provisions and clear what you can do, what they can't do. 2. speech understanding learning series Xdiscipline standards of "four must", the "four upholdings", mastering various types of disciplina-tection Ordinance, mastering selfcipline of the CPC, the CPC disciplinary regulations, members of the Communist Party of China party regulations on rights prodis-lf, maintaining the party Constitution consciousness of the party Constitution. Read through the familiar with the code of seconduct, bearing in mind that oath, clear Members of the standards and conditions, enhance respect, abide by the Constitutionn, good style, deeply understand the conditions, rights and obligations of members, code of the Communist Party of China, and a deep understanding of the party's nature, purpose, guiding principles, goals, organizatio4 【课题】 4.2 纯电阻、纯电感、纯电容电路 【教学目标】 1( 解释纯电阻电路电压、电流大小及相位关系。 2( 解释纯电感电路电压、电流大小及相位关系。 3( 解释纯电容电路电压、电流大小及相位关系。 【教学重点】 1(纯电阻电路电压与电流关系。 2(纯电阻电路的有功功率概念与数学表达式。 3(纯电感电路电压与电流关系。 4(纯电容电路电压与电流关系。 5(纯电感、纯电容电路的无功功率概念与数学表达式。 【教学难点】 纯电阻、纯电感、纯电容电路的电压与电流的关系。 【教学过程】 【一、复习】 1(正弦交流电旋转矢量表示法。 2(电功率的计算方法。 【二、引入新课】 纯电阻是理想元件，但有些实际负载(如电炉)可以看成是纯电阻负载。由于交流电路的特性， 本节将研究电流、电压及功率的瞬时值等。 【三、讲授新课】 4.2.1 纯电阻电路 1、电压与电流的关系 (1)纯电阻电路如图4.9(a)所示。设图示方向为参考方向，电压的初相为零。即 u,Usin,tm Uum根据欧姆定律得 i,,sin,tRR i , Isin, t m (2)纯电阻电路电流和电压关系(波形如图4.9(b)所示)为 1)电压u和电流i的频率相同; 2)电压u和电流i的相位相同; 3)最大值和有效值仍然满足欧姆定律: Um I,mR U I,R XI series read the important speech by General Secretary (2016), XI Henan work research guide, General Secretary's important . Learning series speech, main understand master following aspects content: (1) ideal faithe party spirit, fulfills the purpose ideas, moral character, conservation related to the basic requirements. Learning of the speechhen tharty Central Committee on governance of the new concept of basic elements of new ideas and new strategies, master and strengtderstanding learning series XI series the basic spirit of an important speech by General Secretary, learn to understand the Povisions and clear what you can do, what they can't do. 2. speech undiscipline standards of "four must", the "four upholdings", mastering various types of disciplinary offence and punishment pr-rty regulations on rights protection Ordinance, mastering selfdiscipline of the CPC, the CPC disciplinary regulations, members of the Communist Party of China pa-familiar with the code of self ct, abide by the Constitution, maintaining the party Constitution consciousness of the party Constitution. Read through theresped obligations of members, code of conduct, bearing in mind that oath, clear Members of the standards and conditions, enhance the party's nature, purpose, guiding principles, goals, organization, good style, deeply understand the conditions, rights an the Communist Party of China, and a deep understanding of5 (3)矢量关系如图4.9(c)所示。 (a)电路图 (b)电压和电流的波形 (c)矢量图 图4.9 纯电阻电路 2(功率 (1)瞬时功率:每个瞬间电压与电流的乘积。 p = u, i = U sin, t , I sin, t mm2=UI sin, t m m2= 2 U I sin, t 纯电阻电路瞬时功率的变化曲线如图4.10所示。 图4.10 纯电阻电路有功功率 纯电阻瞬时功率始终在横轴上方，说明它总为正值，它总是在从电源吸收能量，是个耗能元件。 (2)有功功率(平均功率) 有功功率(平均功率):取瞬时功率在一个周期内的平均值其数学表达式为 UImm P,2 或 2U2P UIRI,,,R 有功功率如图4.10所示，是一定值。是电流和电压有效值的乘积，也是电流和电压最大值乘积 的一半。 [4.5] 电炉的额定电压U例, 220 V，额定功率P=1 000 W，把它接到220 V 的工频交流电源N N 上工作。求电炉的电流和电阻值。如果连续使用2 h，它所消耗的电能是多少, [解] 电炉接在220V交流电源上，它就工作在额定状态，这时流过的电流就是额定电流，因为 电炉可以看成是纯电阻负载，所以 P1000NA , 4.55 A I,,NU220N 它的电阻值为 U220, , 48.4 , R,,I4.55 工作2h消耗的电能为 W , Pt , 1000 ， 2 W,h , 2000 W , h , 2 kW,h 4.2.2 纯电感电路 understand master following aspects content: (1) ideal faith by General Secretary (2016), XI Henan work research guide, General Secretary's important speech. Learning series speech, main speechpurpose ideas, moral character, conservation related to the basic requirements. Learning of the XI series read the important e of the new concept of basic elements of new ideas and new strategies, master and strengthen the party spirit, fulfills the ernancI series the basic spirit of an important speech by General Secretary, learn to understand the Party Central Committee on govry offence and punishment provisions and clear what you can do, what they can't do. 2. speech understanding learning series Xdiscipline standards of "four must", the "four upholdings", mastering various types of disciplina-tection Ordinance, mastering selfcipline of the CPC, the CPC disciplinary regulations, members of the Communist Party of China party regulations on rights prodis-lf, maintaining the party Constitution consciousness of the party Constitution. Read through the familiar with the code of seconduct, bearing in mind that oath, clear Members of the standards and conditions, enhance respect, abide by the Constitutionn, good style, deeply understand the conditions, rights and obligations of members, code of the Communist Party of China, and a deep understanding of the party's nature, purpose, guiding principles, goals, organizatio6 2.4.1 电压和电流的关系 (1)纯电感线圈:当线圈的电阻小到可以忽略不计的程度。 设图4.11(a)所示方向为参考方向，电流的初相为零，即 , Isin, t im 经整理可得 πu = L I ,sin(,t，)m2 或 πu , U sin(,t，)m2(2)纯电感电路电流和电压的关系为: 1)电压和电流的频率相同，即同频; ππ2)电压和电流的相位差，电压在相位上超前电流(其波形如图4.11(b)所示); 22 3)电压和电流的最大值之间和有效值之间的关系分别为 U, , L I m m U, XI m L m U , XI L 式中X, , L , 2 , f L称为电感的电抗，简称感抗，感抗的单位是欧[姆](,)。 L 3(电压和电流的矢量关系如图4.11(c)所示。 (a)电路图 (b)电压和电流的波形 (c)矢量图 图4.11 纯电感电路 2(功率 (1)瞬时功率 π , U I sin, t p,u,isin(,t，)mm2 = UI cos, t , sin, t mm p , UIsin2,t变化曲线如图4.12所示。 1)瞬时功率以电流或电压2倍频率变化。 2)当p , 0时，电感从电源吸收电能转换成磁场能储存在电感中;当p , 0时，电感中储存的磁 场能转换成电能送回电源。 3)瞬时功率p的波形在横轴上、下的面积是相等的，所以电感不消耗能量，是个储能元件。 . Learning series speech, main understand master following aspects content: (1) ideal faithspeechXI series read the important speech by General Secretary (2016), XI Henan work research guide, General Secretary's important e party spirit, fulfills the purpose ideas, moral character, conservation related to the basic requirements. Learning of the hen tharty Central Committee on governance of the new concept of basic elements of new ideas and new strategies, master and strengtderstanding learning series XI series the basic spirit of an important speech by General Secretary, learn to understand the Povisions and clear what you can do, what they can't do. 2. speech undiscipline standards of "four must", the "four upholdings", mastering various types of disciplinary offence and punishment pr-rty regulations on rights protection Ordinance, mastering selfdiscipline of the CPC, the CPC disciplinary regulations, members of the Communist Party of China pa-familiar with the code of self ct, abide by the Constitution, maintaining the party Constitution consciousness of the party Constitution. Read through theresped obligations of members, code of conduct, bearing in mind that oath, clear Members of the standards and conditions, enhance the party's nature, purpose, guiding principles, goals, organization, good style, deeply understand the conditions, rights an the Communist Party of China, and a deep understanding of7 图4.12 纯电感电路瞬时功率 (2)有功功率 电感的有功功率根据理论计算可得 p , 0 电感有功功率为零，说明它并不耗能，只是将能量不停地吸收和释放。 (3)无功功率 无功功率:电感与电源之间有能量的往返互换，这部分功率没有消耗掉。互换功率的大小用其瞬 时功率最大值来衡量。 2U2 QUIXI,,,LXL 无功功率的单位用乏[尔](var)表示。 例[4.6] 有一电阻可以忽略的电感线圈，电感L = 300 mH。把它接到u = 220(V)的2sin,t 工频交流电源上，求电感线圈的电流有效值和无功功率。若把它改接到有效值为100 V的另一交流电 源上，测得其电流为0.4 A，求该电源的频率是多少, [解] (1)电压u , 220 (V)的工频交流电压的有效值为220 V，f为50 H 2sin,tZ电感感抗 ,3X, , L , 2 , f L , 2 ， 3.14 ， 50 ， 300 ， 10 , = 94.2 , L 电感电流为 U220A , 2.34 A I,,X94.2L 无功功率为 Q , U I , 220 ， 2.34 var , 514.8 var (2)接100V交流电源时: 电感电抗 U100 , , 250 , X,,LI0.4 电源频率 250XL= Hz , 133 Hz f,,32πL2，3.14，300，10 4.2.3 纯电容电路 1(电流和电压的关系 (1)纯电容电路如图4.13(a)所示。 设图4.13(a)所示方向为参考方向，电压初相为零，即 u = Usin , t m 整理可得 i , , C Ucos , t m πi = Isin (, t +) m 2 (2)纯电容电路电流和电压关系[波形如图4.13(b)所示]为 1)电流和电压的频率相同，即同频; speechpurpose ideas, moral character, conservation related to the basic requirements. Learning of the XI series read the important e of the new concept of basic elements of new ideas and new strategies, master and strengthen the party spirit, fulfills the ernancI series the basic spirit of an important speech by General Secretary, learn to understand the Party Central Committee on govry offence and punishment provisions and clear what you can do, what they can't do. 2. speech understanding learning series Xdiscipline standards of "four must", the "four upholdings", mastering various types of disciplina-tection Ordinance, mastering selfcipline of the CPC, the CPC disciplinary regulations, members of the Communist Party of China party regulations on rights prodis-lf, maintaining the party Constitution consciousness of the party Constitution. Read through the familiar with the code of seconduct, bearing in mind that oath, clear Members of the standards and conditions, enhance respect, abide by the Constitutionn, good style, deeply understand the conditions, rights and obligations of members, code of the Communist Party of China, and a deep understanding of the party's nature, purpose, guiding principles, goals, organizatiounderstand master following aspects content: (1) ideal faith by General Secretary (2016), XI Henan work research guide, General Secretary's important speech. Learning series speech, main 8 πππ，电流在相位上超前电压，即电压在相位上滞后电流; 2)电流和电压的相位互差222 3)电流和电压的最大值之间和有效值之间的关系为 UUmmI= , C U== m m X1C ,C UI, XC 11式中 X=称为电容的电抗，简称容抗，单位为欧[姆](,)。 ,C ,C2πfC (3)电压和电流矢量关系如图4.13(c)所示。 (a)电路图 (b)电压和电流的波形 (c)矢量图 图4.13 纯电容电路 2(功率 (1)瞬时功率 πp = u , i = Usint , Isin (, t ， ) m m 2 =UIsin, t , cos, t m m p = UI sin2, t 变化曲线如图4.14所示。 1)瞬时功率以2倍频变化。 2)当p > 0时，电容从电源吸收电能转换成电场能储存在电容中;当p < 0时，电容中储存的电 场能转换成电能送回电源。 3)电容不消耗电能，是个储能元件。 图4.14 纯电容电路瞬时功率 (2)有功功率 有功功率为零。不耗能，只是将能量不停地吸收和释放。 p = 0 (3)无功功率 电容的无功功率 . Learning series speech, main understand master following aspects content: (1) ideal faithspeechXI series read the important speech by General Secretary (2016), XI Henan work research guide, General Secretary's important e party spirit, fulfills the purpose ideas, moral character, conservation related to the basic requirements. Learning of the hen tharty Central Committee on governance of the new concept of basic elements of new ideas and new strategies, master and strengtderstanding learning series XI series the basic spirit of an important speech by General Secretary, learn to understand the Povisions and clear what you can do, what they can't do. 2. speech undiscipline standards of "four must", the "four upholdings", mastering various types of disciplinary offence and punishment pr-rty regulations on rights protection Ordinance, mastering selfdiscipline of the CPC, the CPC disciplinary regulations, members of the Communist Party of China pa-familiar with the code of self ct, abide by the Constitution, maintaining the party Constitution consciousness of the party Constitution. Read through theresped obligations of members, code of conduct, bearing in mind that oath, clear Members of the standards and conditions, enhance the party's nature, purpose, guiding principles, goals, organization, good style, deeply understand the conditions, rights an the Communist Party of China, and a deep understanding of9 2U2 I = Q = UI = XC XC 其单位是乏[尔](var)。 例[4.7] 有一个50μF的电容器，接到u , 220 sin,t V工频交流电源上，求电容的电流有效2 值和无功功率。若将交流电压改为500 Hz时，求通过电容器的电流为多少, [解] (1)电压u =220sinωt V工频交流电压的有效值为220 V，频率为50 Hz，电容容抗为 2 111= , , 64 , X=,C ,6,C2πfC2，3.14，50，50，10 电容电流为 U220I , , A , 3.4 A X64C 无功功率为 Q = UI = 220 ， 3.4 var = 748 var (2)当f , 500 Hz时 电容容抗为 111X== , = 6.4 , ,C ,6,C2πfC2，3.14，500，50，10 通过电容的电流 U220I == A , 34.4 A X6.4C 【四、小结】 (掌握纯电阻电路中电压和电流的关系，以及纯电阻电路的有功功率。 1 2(掌握纯电感电路中电压和电流的关系，以及纯电感电路的无功功率。 3(掌握纯电容电路中电压和电流的关系，以及纯电容电路的无功功率。 【五、习题】 一、是非题:4、5、6;二、选择题:5、6;三、计算题:1、2;四、作图题:3、4。 understand master following aspects content: (1) ideal faith by General Secretary (2016), XI Henan work research guide, General Secretary's important speech. Learning series speech, main speechpurpose ideas, moral character, conservation related to the basic requirements. Learning of the XI series read the important e of the new concept of basic elements of new ideas and new strategies, master and strengthen the party spirit, fulfills the ernancI series the basic spirit of an important speech by General Secretary, learn to understand the Party Central Committee on govry offence and punishment provisions and clear what you can do, what they can't do. 2. speech understanding learning series Xdiscipline standards of "four must", the "four upholdings", mastering various types of disciplina-tection Ordinance, mastering selfcipline of the CPC, the CPC disciplinary regulations, members of the Communist Party of China party regulations on rights prodis-lf, maintaining the party Constitution consciousness of the party Constitution. Read through the familiar with the code of seconduct, bearing in mind that oath, clear Members of the standards and conditions, enhance respect, abide by the Constitutionn, good style, deeply understand the conditions, rights and obligations of members, code of the Communist Party of China, and a deep understanding of the party's nature, purpose, guiding principles, goals, organizatio10 【课题】 4.3 电阻与电感串联电路 【教学目标】 解释电阻与电感串联电路电压、电流大小及相位关系。 【教学重点】 R、L串联电路的电压三角形、阻抗三角形和功率三角形的意义。 【教学难点】 1(R、L串联电路的阻抗性质。 2(R、L串联电路的有功功率。 3(R、L串联电路的无功功率。 【教学过程】 【一、复习】 1(纯电阻电路。 2(纯电感电路。 3(纯电容电路。 【二、引入新课】 纯电阻、纯电感和纯电容元件的性质对本节电阻与电感串联电路的分析有基础性的作用。但是电 阻和电感元件串连后，会出现一些新问题，因此需要引出新概念和新的分析方法。 【三、讲授新课】 4.3.1 电流和电压的关系 1(电感串联电路如图4.15所示。 图4.15 R、L串联电路 设电路中电流为 i = Isin, t m 则， u= Usin, t R R m πu=Usin ( , t ， ) LLm 2并且 πu = u + u= Usin, t + Usin ( , t + ) RL R mL m 2 u =Usin ( , t + , ) m 2(矢量图如图4.16所示。 . Learning series speech, main understand master following aspects content: (1) ideal faithspeechXI series read the important speech by General Secretary (2016), XI Henan work research guide, General Secretary's important e party spirit, fulfills the purpose ideas, moral character, conservation related to the basic requirements. Learning of the hen tharty Central Committee on governance of the new concept of basic elements of new ideas and new strategies, master and strengtderstanding learning series XI series the basic spirit of an important speech by General Secretary, learn to understand the Povisions and clear what you can do, what they can't do. 2. speech undiscipline standards of "four must", the "four upholdings", mastering various types of disciplinary offence and punishment pr-rty regulations on rights protection Ordinance, mastering selfdiscipline of the CPC, the CPC disciplinary regulations, members of the Communist Party of China pa-familiar with the code of self ct, abide by the Constitution, maintaining the party Constitution consciousness of the party Constitution. Read through theresped obligations of members, code of conduct, bearing in mind that oath, clear Members of the standards and conditions, enhance the party's nature, purpose, guiding principles, goals, organization, good style, deeply understand the conditions, rights an the Communist Party of China, and a deep understanding of11 图4.16 R、L串联电路矢量图 由矢量图可见: (1)电源电压矢量为电阻电压和电感电压矢量之和。 U , U ， U RL 根据矢量图可得 22U = U，URL UL, = arctan UR可得电压三角形，如图4.17(a)所示。 (2)阻抗 2222U = = I R，XU，URLL U = |Z| I 阻抗Z、电阻R和感抗X也可构成一个与图4.17(a)相似的三角形，如图4.17(b)所示，但L 这个三角形不是矢量。 (a)电压三角形 (b)阻抗三角形 (c)功率三角形 图4.17 R、L串联电路三角形 XL, , arctan R 4.3.2 功率 1(有功功率 电阻是耗能元件，即电阻消耗的功率就是该电路的有功功率。 P =I U=I U cos , R 式中 U= U cos , 可看成是总电压U的有功分量。 R ,cos为功率因数，用字母,表示，即 , , cos , , 称为功率因数角。 2(无功功率 Q , I U , I U sin , L ,式中 U=U sin可看成是总电压U的无功分量。 L 另外根据Q = IU可得 L 2Q = ( I X) I ,X I LL 3(视在功率 S , U I 视在功率的单位是伏安(V , A)。 understand master following aspects content: (1) ideal faith by General Secretary (2016), XI Henan work research guide, General Secretary's important speech. Learning series speech, main speechpurpose ideas, moral character, conservation related to the basic requirements. Learning of the XI series read the important e of the new concept of basic elements of new ideas and new strategies, master and strengthen the party spirit, fulfills the ernancI series the basic spirit of an important speech by General Secretary, learn to understand the Party Central Committee on govry offence and punishment provisions and clear what you can do, what they can't do. 2. speech understanding learning series Xdiscipline standards of "four must", the "four upholdings", mastering various types of disciplina-tection Ordinance, mastering selfcipline of the CPC, the CPC disciplinary regulations, members of the Communist Party of China party regulations on rights prodis-lf, maintaining the party Constitution consciousness of the party Constitution. Read through the familiar with the code of seconduct, bearing in mind that oath, clear Members of the standards and conditions, enhance respect, abide by the Constitutionn, good style, deeply understand the conditions, rights and obligations of members, code of the Communist Party of China, and a deep understanding of the party's nature, purpose, guiding principles, goals, organizatio12 22 S =P，Q 由S 、P和Q可构成功率三角形，如图4.17(c)所示。 Q, , arctan P 视在功率表征的是电源设备的容量。 o[例4.8] 电阻和电感串联电路，已知感抗 X =6.24 k,，电流滞后电压82，试求电阻值。 L XL[解] 根据= arctan可得 ,R XLtan , , R 3XL6.24，10R , , , , 877 , tan,tan82: [例4.9] 对于实际的电感线圈可以通过测量电压和电流，进而求得线圈的电阻R和电感L 。其方法是:给线圈加直流电压12 V，测得流过线圈的直流电流I = 2 A;给线圈加交流工频220 V 电压，测得有效值电流I = 22 A。写出电阻R和电感L求解步骤。 [解] 先求电阻R，根据欧姆定律可得 U12R = =, = 6 , I2 220U|Z|= = Ω = 10 , I22 222210,6X , , , , 8 , |Z|,RL 电感L根据X =ωL得 L X8LL , = H , 0.025 H 2，3.14，50, [例4.10] 某电动机接在220 V工频交流电源上可获得14 A电流，连接在电动机线路中的功率表显示功率为2.5 kW，试求该电动机的视在功率S 、无功功率Q和功率因数角 ,。 [解] S , UI , 220 ， 14 V,A , 3 080 V,A=3.08 kV,A P = U I cos , = S cos, P2.5cosφ = , , 0.812 S3.08 , , 35.7: Q = U I sin , , S sin , , 3.08 ， sin 35.7 º kvar =1.8 kvar 【四、小结】 QUXLL1(电阻与电感串联电路电压与电流有相位差φ。φ , arctan , arctan , arctan 。 PRUR 22U，U2(电感电压、电阻电压与电源电压之间关系符合电压三角形。U =。 RL 22R，X3(感抗、电阻和阻抗之间关系符合阻抗三角形。,Z, =。 L 22P，Q4(有功功率、无功功率和视在功率之间关系符合功率三角形。S=。 【五、习题】 一、是非题:7;二、选择题:7;三、计算题:3。 . Learning series speech, main understand master following aspects content: (1) ideal faithspeechXI series read the important speech by General Secretary (2016), XI Henan work research guide, General Secretary's important e party spirit, fulfills the purpose ideas, moral character, conservation related to the basic requirements. Learning of the hen tharty Central Committee on governance of the new concept of basic elements of new ideas and new strategies, master and strengtderstanding learning series XI series the basic spirit of an important speech by General Secretary, learn to understand the Povisions and clear what you can do, what they can't do. 2. speech undiscipline standards of "four must", the "four upholdings", mastering various types of disciplinary offence and punishment pr-rty regulations on rights protection Ordinance, mastering selfdiscipline of the CPC, the CPC disciplinary regulations, members of the Communist Party of China pa-familiar with the code of self ct, abide by the Constitution, maintaining the party Constitution consciousness of the party Constitution. Read through theresped obligations of members, code of conduct, bearing in mind that oath, clear Members of the standards and conditions, enhance the party's nature, purpose, guiding principles, goals, organization, good style, deeply understand the conditions, rights an the Communist Party of China, and a deep understanding of13 【课题】 , 4.4 电阻、电感和电容串联电路及谐振 【教学目标】 了解电阻、电感和电容串联电路电压、电流大小及关系。描述串联谐振。 【教学重点】 1(电路呈现的三种性质的分析。 2(串联谐振。 【教学难点】 1(电路呈现的三种性质。 2(串联谐振时品质因数和谐振频率。 【教学过程】 【一、复习】 1(电阻和电感串联电路电流与电压关系。 2(电阻和电感串联电路电压三角形、阻抗三角形、功率三角形。 【二、引入新课】 如果在电阻和电感串联电路的基础上再增加一个电容元件，电路所表现出的各种特征会有很大的 差异，一些物理现象的原因和解释都更加复杂，例如谐振现象。 【三、讲授新课】 4.4.1 电流与电压的关系 1(电路如图4.18所示，设电路中电流初相角为零，即 i = Isin, t m 那么 u= Usinωt =R I sin, t R R m m ππu= Usin (, t + ) = X I sin (, t + ) L L m Lm 22 ππu= Usin (, t ,) = XI sin (, t ,) C C m C m 22 u = u+ u+ u R L C ππ=Usin , t ， Usin (, t + ) + Usin (, t ,) Rm Lm C m 22 u = Usin (, t + , ) m understand master following aspects content: (1) ideal faith by General Secretary (2016), XI Henan work research guide, General Secretary's important speech. Learning series speech, main speechpurpose ideas, moral character, conservation related to the basic requirements. Learning of the XI series read the important e of the new concept of basic elements of new ideas and new strategies, master and strengthen the party spirit, fulfills the ernancI series the basic spirit of an important speech by General Secretary, learn to understand the Party Central Committee on govry offence and punishment provisions and clear what you can do, what they can't do. 2. speech understanding learning series Xdiscipline standards of "four must", the "four upholdings", mastering various types of disciplina-tection Ordinance, mastering selfcipline of the CPC, the CPC disciplinary regulations, members of the Communist Party of China party regulations on rights prodis-lf, maintaining the party Constitution consciousness of the party Constitution. Read through the familiar with the code of seconduct, bearing in mind that oath, clear Members of the standards and conditions, enhance respect, abide by the Constitutionn, good style, deeply understand the conditions, rights and obligations of members, code of the Communist Party of China, and a deep understanding of the party's nature, purpose, guiding principles, goals, organizatio14 图4.18 R、L、C串联电路 2(矢量图，如图4.19所示(设X > X，即U> U)。 LCL C 图4.19 R、L、C串联电路矢量图 由矢量图可见: (1)电源电压矢量为电阻、电感和电容电压矢量之和 U , U， U ， U R LC由矢量图可得 22U = U，(U,U)RLC U,ULC, , arctan UR可得电压三角形，如图4.20(a)所示。 (a)电压三角形 (b)阻抗三角形 (c)功率三角形 图4.20 R、L、C串联电路三角形 (2)阻抗 2222U =U，(U,U)= IR，(X,X) RLCLC 22R，XU = I = |Z | I 阻抗Z、电阻R和电抗X构成一个与图4.20(a)相似的三角形，如图4.20(b)所示，这个三角 形不是矢量。 . Learning series speech, main understand master following aspects content: (1) ideal faithspeechXI series read the important speech by General Secretary (2016), XI Henan work research guide, General Secretary's important e party spirit, fulfills the purpose ideas, moral character, conservation related to the basic requirements. Learning of the hen tharty Central Committee on governance of the new concept of basic elements of new ideas and new strategies, master and strengtderstanding learning series XI series the basic spirit of an important speech by General Secretary, learn to understand the Povisions and clear what you can do, what they can't do. 2. speech undiscipline standards of "four must", the "four upholdings", mastering various types of disciplinary offence and punishment pr-rty regulations on rights protection Ordinance, mastering selfdiscipline of the CPC, the CPC disciplinary regulations, members of the Communist Party of China pa-familiar with the code of self ct, abide by the Constitution, maintaining the party Constitution consciousness of the party Constitution. Read through theresped obligations of members, code of conduct, bearing in mind that oath, clear Members of the standards and conditions, enhance the party's nature, purpose, guiding principles, goals, organization, good style, deeply understand the conditions, rights an the Communist Party of China, and a deep understanding of15 XXX,LC, = arctan , arctan RR 4.4.2 功率 1(有功功率 电阻是耗能元件，即电阻消耗的功率就是该电路的有功功率 P = I U= I U cos , R 可看作是总电压U的有功分量; 是电路的功率因数角。 式中 U= U cos ,,R 2(无功功率 在电阻、电感和电容串联电路中，电感和电容都与电源进行能量交换，当电感吸收能量时(P> 0)，L 此时电容正好从释放能量(P, 0);反之电容吸收能量时(P> 0)，电感释放能量(P< 0)，它C C L 们之间进行能量交换的差值才与电源进行交换。即只有当电感和电容相互交换能量不足部分，才与电 源进行交换，所以整个电路的无功功率为 Q = Q, Q L C = ( U, U ) I L C = U IX Q= U I sin , 3(视在功率 根据视在功率的定义可知 S = U I 其单位是伏安(V , A)。 2222 S,P，Q,P，(Q,Q)LC 由S、P、Q可构成功率三角形如图4.20(c)所示。 功率三角形不是矢量三角形，并且与电压三角形、阻抗三角形相似，可得 QQQ,LC, = arctan ,arctanPP 4.4.3 电路呈现的三种性质 由于R、L、C及f 等参数的不同，电路对外会分别呈现出三种不同的性质。 (1)呈感性 当X>X时，则U>U，Q>Q 电路呈感性，电路中电压超前电流，其矢量 LCLC L C 图如图4.21(a)所示。 (2)呈容性 当X< X时，则U要求

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